Looks like a magic square, but can't solve it, please help.

Question

A friend sent me this from her game

I tried many combinations and I cannot solve it for the life of me.

9 squares starting from each corner is (top left 61, top right 61, bottom left 69, bottom right 61 without the ?)

Down 30 11 41 23?

Across 20 35 29 21?

I tried adding, subtracting, this to an extent Find missing number in grid., etc.

What type of problem is this called? How do you solve it?

I told her to pick 20 since I see no pattern, but 20 is the only available number to keep the pattern for the numbers i added across and downward.

Thanks.

Answer 1

You are just supposed to find some pattern that fits the given data. In this case if you multiply the first two columns and subtract the third you get the fourth. So $7 \times 4-10=18$. Hopefully there is one pattern that is much simpler than the others justifying one answer.

Answer 2

The correct answer is $18 $

Note that the product of the first two terms of each row is ths same as the sum of the other two terms of the same row.

$6\times 2 = 5+7$, $ 8\times 3=17+7$, $ 9\times 2 = 9+9$,$ 7\times 4=10+18$